2,080 research outputs found
Skyrmions, Spectral Flow and Parity Doubles
It is well-known that the winding number of the Skyrmion can be identified as
the baryon number. We show in this paper that this result can also be
established using the Atiyah-Singer index theorem and spectral flow arguments.
We argue that this proof suggests that there are light quarks moving in the
field of the Skyrmion. We then show that if these light degrees of freedom are
averaged out, the low energy excitations of the Skyrmion are in fact spinorial.
A natural consequence of our approach is the prediction of a state
and its excitations in addition to the nucleon and delta. Using the recent
numerical evidence for the existence of Skyrmions with discrete spatial
symmetries, we further suggest that the the low energy spectrum of many light
nuclei may possess a parity doublet structure arising from a subtle topological
interaction between the slow Skyrmion and the fast quarks. We also present
tentative experimental evidence supporting our arguments.Comment: 22 pages, LaTex. Uses amstex, amssym
Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
Field theories on the Groenewold-Moyal(GM) plane are studied using the
Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields
is treated in detail. The S-matrix elements in this non-perturbative approach
are shown to be equal to the interaction representation S-matrix elements. This
is a new non-trivial result: in both cases, the S-operator is independent of
the noncommutative deformation parameter and the change in
scattering amplitudes due to noncommutativity is just a time delay. This result
is verified in two different ways. But the off-shell Green's functions do
depend on . In the course of this analysis, unitarity of the
non-perturbative S-matrix is proved as well.Comment: 18 pages, minor corrections, To appear in Phys. Rev. D, 201
Quantum Fields with Noncommutative Target Spaces
Quantum field theories (QFT's) on noncommutative spacetimes are currently
under intensive study. Usually such theories have world sheet noncommutativity.
In the present work, instead, we study QFT's with commutative world sheet and
noncommutative target space. Such noncommutativity can be interpreted in terms
of twisted statistics and is related to earlier work of Oeckl [1], and others
[2,3,4,5,6,7,8]. The twisted spectra of their free Hamiltonians has been found
earlier by Carmona et al [9,10]. We review their derivation and then compute
the partition function of one such typical theory. It leads to a deformed black
body spectrum, which is analysed in detail. The difference between the usual
and the deformed black body spectrum appears in the region of high frequencies.
Therefore we expect that the deformed black body radiation may potentially be
used to compute a GZK cut-off which will depend on the noncommutative parameter
.Comment: 20 pages, 5 figures; Abstract changed. Changes and corrections in the
text. References adde
Twisted Poincar\'e Invariant Quantum Field Theories
It is by now well known that the Poincar\'e group acts on the Moyal plane
with a twisted coproduct. Poincar\'e invariant classical field theories can be
formulated for this twisted coproduct. In this paper we systematically study
such a twisted Poincar\'e action in quantum theories on the Moyal plane. We
develop quantum field theories invariant under the twisted action from the
representations of the Poincar\'e group, ensuring also the invariance of the
S-matrix under the twisted action of the group . A significant new contribution
here is the construction of the Poincar\'e generators using quantum fields.Comment: 17 pages, JHEP styl
Topology in Physics - A Perspective
This article, written in honor of Fritz Rohrlich, briefly surveys the role of
topology in physics.Comment: 16pp, 2 figures included (encapsulated postscript
Hypothesis Testing For Network Data in Functional Neuroimaging
In recent years, it has become common practice in neuroscience to use
networks to summarize relational information in a set of measurements,
typically assumed to be reflective of either functional or structural
relationships between regions of interest in the brain. One of the most basic
tasks of interest in the analysis of such data is the testing of hypotheses, in
answer to questions such as "Is there a difference between the networks of
these two groups of subjects?" In the classical setting, where the unit of
interest is a scalar or a vector, such questions are answered through the use
of familiar two-sample testing strategies. Networks, however, are not Euclidean
objects, and hence classical methods do not directly apply. We address this
challenge by drawing on concepts and techniques from geometry, and
high-dimensional statistical inference. Our work is based on a precise
geometric characterization of the space of graph Laplacian matrices and a
nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate
our resulting methodologies for testing in the context of networks derived from
functional neuroimaging data on human subjects from the 1000 Functional
Connectomes Project. In particular, we show that this global test is more
statistical powerful, than a mass-univariate approach. In addition, we have
also provided a method for visualizing the individual contribution of each edge
to the overall test statistic.Comment: 34 pages. 5 figure
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